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was not part of .this pattern. In another direction he also
departed occasionally from Ms principal interests when,
according to the fashion of his times, he occupied himself with
the purely mathematical aspects of certain problems (in the
theory of attraction as in Newton's gravitation) of mathema-
tical physics. His contributions in this field were of mathema-
tical rather than physical interest.
Up till the last decade of his life Kroneeker was a free man
with obligations to no employer. Nevertheless he voluntarily
assumed scientific duties, for which he received no remunera-
tion, when he availed himself of his privilege as a member of the
Berlin Academy to lecture at the University of Berlin. From
1861 to 1883 he conducted regular courses at the university,
principally on his personal researches, after the necessary intro-
ductions. In 1883 Kurnmer, then at Berlin, retired, and
Kronecker succeeded his old master as ordinary professor. At
this period of his life he travelled extensively and was a frequent
and welcome participant in scientific meetings in Great Britain,
France, and Scandinavia.
Throughout his career as a mathematical lecturer Kronecker
competed with "VTeierstrass and other celebrities whose subjects
were more popular than his own. Algebra and the theory of
numbers have never appealed to so wide an audience as have
geometry and analysis, possibly because the connexions of the
latter with physical science are more apparent.
Kronecker took his aristocratic isolation good-naturedly and
even with a certain satisfaction. His beautifully clear introduc-
tions deluded his auditors into a belief that the subsequent
course of lectures would be easy to follow* This belief evapor-
ated rapidly as the course progressed, until after three sessions
all but a faithful and obstinate few had silently stolen away -
many of them to listen to Weierstrass. Kronecker rejoiced. A
curtain could now be drawn across the room behind the first
few rows of chairs, he joked, to bring lecturer and auditors into
cosier intimacy. The few disciples he retained followed him
devotedly, walking home with him to continue the discussions
of the lecture room and frequently affording the crowded side-
walks of Berlin the diverting spectacle of an excited little man